Science isn't a body of facts, science is a process for figuring out how the world works: you see something interesting, come up with an idea of why that might happen, and test you're idea to see if you're right. You repeat this process until you figure out why things happen the way they do, and then you use that knowledge to explain new things, or to do things that you couldn't do before.
So, when I tell you to think like a scientist, what I'm saying is to use that process, which is something anybody can do. You don't need to be good at math, or take a bunch of classes--you just need to observe the world around you, ask questions, and look for answers.
Think Like a Scientist
From Prof. Chad Orzel's Graduation Speech: